Should "wage war with" be taken to mean against, or does it mean "wage war in union with the Germans, (ie together against other tribes)? I presume the former, but the latter could be implied by the English translation.

You are right to notice the ambiguity in English.
The Latin itself is a bit odd, in that since the case dependent on bellum gerere is in the relative, the usual preposition in either the form of "cum+abl." or "contra+acc." has been removed, and we are left with an ablative (with cum understood; a dative is unlikely).
Based upon the common usage of "bellum gerere" and knowledge of history, we know this means that the two armies continually fought against one another.

Bellum gerere can also be in the sense "carry on wars [repeatedly]" which makes sense. And bene gerere is to carry out successfully. Which is somewhat random but interesting. It's one of my favourite idioms, along with "longe lateque", "Everywhere".

I was wondering, "did Celts and Germans, as Caesar defined them, ever unite to fight, say, another Celtic tribe?" The more I research the Celts, the less I can say with certainty about them. I don't believe there was just one large group all considering them "Celts."

Episcopus, as another aside, Nietzsche's etymology of modern Italian bella, etc, "beautiful," was that it came from bellum. Perhaps war itself was seen as a thing of beauty to the Roman mind.

In Belgium Caesar's Gallic war is on the program of the fourth year Latin. We have to read it. The name 'Belgium' is derived from the title of Caesar's work: take the first 3 letters of bellum and the first two of gallicum and you have belga yet.

Also it's a bit of local history. And in Belgium almost everyone knows the sentence 'Horum omnium fortissimi sunt Belgae'. Caesar continues with the reasons why (propterea quod ...), buts it's just a few of the Belgian people who knows those reasons!

In this text 'bellum gerere cum' really means 'a war

against someone'.

Caesar sais that the Belgians are proximi Germanis.
That's one of the reasons they are so brave! What's brave about being proximi to someone? It can only be brave, if the Germani are a terrifying nation! Caesar wants to tell us that the Germani win every war. But not when they fight with the Belgae. That's why the Belgae are so brave.
And then he emphasizes this by saying they make always war with them 'quibuscum continenter bellum gerunt. And then he mentions that also the Helvetii make war with the Germani (fere cotidianis proeliis cum Germanis contendunt). And this also mean that the Germani couldn't win from the Belgae. Cause otherwise, they would have fight just one war and that's it. When you are the winner there is no reason to keep fighting.

If we presume the Belgians to be together in a war against someone else, why does Caesar not mention against whom? And what's so brave about fighting together (against someonehe he does not mention!)? And why does he mention that they are proximi and what's so brave about that?
When we use this interpretation, this makes no sense.